Sure – action hooks are places you can hook a function to to do certain things, in this case look at if a user is changing information, and then if so, sending an email.
Take a look at the WP Codex for information on add_action.
For example, you are going to hook a function to the wpmem_pre_update_data hook it would be something like:
add_action( 'wpmem_pre_update_data', 'my_function' );
Then my_function could look at the existing data that a user has in the db, to determine if what they are submitting is in any way different.
Then you would write a second function and hook it to wpmem_post_update_data (which comes after the action data has been updated).
add_action( 'wpmem_post_update_data', 'my_other_function' );
In my_other_function, you would send and email (probably using wp_mail) if my_function resulted in a situation where data was in fact being updated.
Note: it will be important to reference the hook documentation referenced above for these hooks – they are similar – so that you know what parameters are passed to the action. In this case, $fields is passed, which is an array containing all of the posted data.